The augmented matrix of the system of equation is written as

\([(5,7,-36),(-8,-11,57)][(38),(-60)]\)

\([(5,7,-36),(-8,-11,57)][(38),(-60)]\)

Question

asked 2021-03-05

Find the augmented matrix for the following system of linear equations:

3x+7y-20z=-4

5x+12y-34z=-7

3x+7y-20z=-4

5x+12y-34z=-7

asked 2020-11-10

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations.
\(\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases}\)

asked 2020-11-06

A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio \(x_1\)

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

asked 2020-10-19

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer \(x_1\) (in $1000) and on the square footage of the home \(x_2 (\text{ in } 100ft^2)\) according to \(y=ax_1+bx_2+c\)

The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the purchase price for a buyer who makes $100000 per year and wants a \(2500ft^2\) home.

The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the purchase price for a buyer who makes $100000 per year and wants a \(2500ft^2\) home.

asked 2020-11-09

Write the augmented matrix for the system of linear equations

2y-z=7

x+2y+z=17

2x-3y+2z=-1

2y-z=7

x+2y+z=17

2x-3y+2z=-1

asked 2021-03-04

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations.

\(\displaystyle{\left\lbrace\begin{matrix}{x}+{y}={0}\\{5}{x}-{2}{y}-{2}{z}={12}\\{2}{x}+{4}{y}+{z}={5}\end{matrix}\right.}\)

\(\displaystyle{\left\lbrace\begin{matrix}{x}+{y}={0}\\{5}{x}-{2}{y}-{2}{z}={12}\\{2}{x}+{4}{y}+{z}={5}\end{matrix}\right.}\)

asked 2021-01-16

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.
Write the solution in vector form.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}&{0}&−{1}&{3}&{9}\backslash{0}&{1}&{2}&−{5}&{8}\backslash{0}&{0}&{0}&{0}&{0}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\)

asked 2021-01-10

Given a linear system of equations below. The matrix equation of the linear system is given by: (see image)

Given a linear system of equations below.The matrix equation of the linear system is given by:Ax=b.The determinant of A is 8.Using Cramers's rule find the value for x.

x+3y+4z=3

2z+6y+9z=5

3x+y-2z=7

Given a linear system of equations below.The matrix equation of the linear system is given by:Ax=b.The determinant of A is 8.Using Cramers's rule find the value for x.

x+3y+4z=3

2z+6y+9z=5

3x+y-2z=7

asked 2021-02-25

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations
\(\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases}\)

asked 2021-02-08

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
\(\begin{bmatrix}1&0&-1&-2&0\\0&1&2&3&0\end{bmatrix}\)